Question regarding books for commutative algebra

Question

So I was searching about books for commutative algebra. I have read most of the algebra namely galois theory and field theory and basic algebra from Dummit Foote. So I was thinking about studying commutative algebra from Dummit Foote. Although most of the suggestion I have seen for the book for commutative algebra is Atiyah Mcdonald. So it will be great if anyone can tell me how well commutative algebra is written in Dummit Foote.

Answer 1

May be its a bit late to comment,but you can go through Basic Commutative Algebra by Dr. Balwant Singh. It is a great commutative algebra book and also covers some interesting topics in Homological Algebra. Dummit and Foote is a great book in its own right but certain things like resolutions, category theory, derived functors are well written in Balwant Singh book.

Answer 2

Dummit and Foote is actually a pretty decent book to learn commutative algebra though I have found that not many people recommend it. It treats basic commutative algebra(including computational aspects of Grobner bases, primary decomposition), affine algebraic geometry(Spec, Zariski topology, Nullstellensatz, localization etc.) and does a decent job of introducing homological algebra. However, I think in regards to certain topics like exact sequences, Hom-Tensor adjunction, Atiyah-Macdonald and Eisenbud's books had more interesting exercises. Another resource which is woefully underappreciated as a reference to commutative algebra is the Stacksproject, chapter 10. Like Eisenbud, it probably contains far too many things that are irrelevant if one has the intention to gain the prerequisites to start learning algebraic geometry but they are still useful references.